This is my guide to playing Orianna. I am by no means a definitive expert on the subject but I've found this build to work wonders. Alot of playing Orianna well is team synergy and ball placement as opposed to item builds or skill sets, so there is alot of trial and error but that's part of the challenge, right?

Your CORE items are Shurelyas Reverie, Rylais Crystal Scepter and Eleisas Miracle.

-Order:

I usually go Elisas, Shurelyas and then Rylais. Really though, feel free to mix it up depemding on how your team is doing


-Why we want Shurelyas:
Simply put, this item maximizes our strengths and minimizes our weaknesses. Oriannas biggest strength is CC in the form of her Command:Shockwave and Command:Dissoance. One of her biggest weaknesses is her squishy nature. Shurelyas has a BUILT IN movement buff which combined with Dissonance makes an ally move ALMOST DOUBLE his or her movement speed. And the mana regen is terrific on her. And the Health and Health regen help her not get shredded by those pesky enemy carries. Just awesome.

-Why we want Rylais:
Once again, we play to our strengths with the slow and reduce our squishiness all in one item. The AP is just gravy.

-Why we want Elisas:
Mana and health regen per second, less Ryzes stunning your face. Need I say more?

[STARTING ITEMS]-
2 fairy charms with three hp potions. All day. They build into Philosophers Stones which build into Elisas and Rylais. Perfect fit for what were doing

[BOOTS]-
I usually go with Sorc Shoes when I'm feelin cocky but in games where things aren't going so hot Ionian Boots of Lucidity are the obvious choice.

[END GAME]-
A Lich Bane plays well with our Core as does a Morello's Evil Tome, but by this point you should be winning the game outright so it shouldn't really be a huge issue.

Go Attack first, then Dissonance then Protect. Alternate Dissonance and Protect till you get your Ult and then pick up another rank in Attack. Then alternate Dissonance and Protect again. The skill priorities go like this: Shockwave>Dissonance>Protect>Attack. So long as you remember that you'll be good!

Up to you and your play style. I tend to go teleport and flash but feel free to add in Cleanse or Ghost or Exhaust. All are good choices as Orianna.

Farming with Orianna is superb! Her Command:Attack works wonders at harass, zoning and farming. When combined with Command:Dissonance she stacks up with some of the best!

Try to take a side lane with a tank if possible. That is your wheelhouse. Stand behind them and harass with Command:Attack and Command:Dissonance, when they initiate attach the ball to them with Command:Protect and then use Command:Dissonance to speed up your partner while slowing down a fleeing enemy. Use Command:Attack when they get too far away for Dissonance. It is really exactly where you want to be.

DONT TAKE MID!! Remember your job is to Support! Yes you can be a ranged caster and take mid and be pretty solid given the right build but Orianna is more of an asset as a Support. Feel free to gank the living **** out of the opponent at middle though, as with your Command:Attack and Command:Dissonance skills you can have a viable gank as early as level 2 if the situation is right for it!

NEVER LET YOUR BALL SIT IDLE DURING TEAM FIGHTS! IT WILL AND YOU SHOULD FEEL VERY BAD ABOUT IT!

There is a right way and a wrong way to play Orianna in team fights. The wrong way is to use Command:Attack right off the bat and then Command:Dissonance and play like you are some sort of ranged-carry-mage-nuke-stunner-thing. You are not that, you are Orianna and YOU want to play like the sort of Gosu pro that you are.

To that end, your first step is to identify who will initiate team fights. That person and you are destined to be best friends, because your second step is WHENEVER they initiate combat have your ball on them with Protect and hit your Ultimate and then spam Dissonance like its your job. When you see then running, and they will run if they are still alive, hit them with a Command Attack in front of them and then spam Dissonance some more. They will QQ then GG.
BUT YOU ARE A SUPPORT CHAMPION SO your second (AND MOST IMPORTANT) step is to identify who is getting ff'd and make sure to watch that(those) person(people) like a hawk. Whenever your ball is idle, you are doing it wrong and it should be Protecting that champion(s) like he is its loving child. You need to remember that you are there so your team can stay there and that keeping people alive is job one. Just because chronologically you start a team fight doing cc and damage does not make it more important.
Your third step is zoning, and this requires finesse. You need to ask questions in this part, questions like "Is that champ going to run away?" "Can my amumu make it back to our turret?" and MOST IMPORTANTLY "Where will my ball do the most good?" Generally the answer to that is just in front of the champion. An enemy gun get away? Plop a Dissonance right in front of them. Amumu getting chased? Dissonance right in front! Then Attack back through and Ult if ya got it to draw them back but of most importance is that when its needed that Dissonance is right in front of that Champion. and remember:
NEVER LET YOUR BALL SIT IDLE IN TEAM FIGHTS! EVER!